where \({\rm d}^{\mathbb {L}}\)  is the weighted Lie algebroid exterior derivative (REF ).
Taking into account the fact that \(\varepsilon \)  is a scalar field, we can interpret this as a Maurer-Cartan equation
(since the commutator term in the usual Maurer-Cartan eq. vanishes because \(\varepsilon \)  is a scalar).
The reason for interpreting (REF ) in such a way is that it
fits with the usual theory of integrable deformations of complex structures (see e.g. [1]}).
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